Physics-Informed Foresight Pruning for Sparse PINN Solvers of Nonlinear PDEs

• URL: http://arxiv.org/abs/2608.25564v1
• Date: Wed, 26 Aug 2026 09:16:24 GMT
• Title: Physics-Informed Foresight Pruning for Sparse PINN Solvers of Nonlinear PDEs
• Abstract summary: We introduce physics-informed spectrum-aware pruning (PI-SAP) for sparse PirateNet PDE solvers.<n>Experiments show PI-SAP more consistently preserves Gray-Scott residual fidelity and is competitive under aggressive sparsity.<n>Small-batch PINN-NTK diagnostics further show that residual fidelity, solution accuracy, and kernel conditioning are distinct objectives.
• Score: 8.49003726182843
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Physics-informed neural networks (PINNs) often rely on over-parameterized models to optimize coupled solution and differential-residual objectives, leaving unclear how much capacity is necessary and what pruning should preserve. We study foresight pruning at initialization for sparse PirateNet PDE solvers. Standard neural tangent kernel spectrum-aware pruning (NTK-SAP) aims to preserve output-side training dynamics but may overlook parameters whose main influence arises through derivatives in the governing equations. We introduce physics-informed spectrum-aware pruning (PI-SAP), which assigns saliency using sensitivity of the PDE residual. Experiments on the Gray-Scott equations, complex Ginzburg-Landau equation, Burgers' equation, and linear convection equation show that PI-SAP more consistently preserves Gray-Scott residual fidelity and is competitive under aggressive sparsity. However, no criterion is uniformly optimal across equations or sparsity levels. Small-batch PINN-NTK diagnostics further show that residual fidelity, solution accuracy, and kernel conditioning are distinct objectives, motivating pruning methods that explicitly balance solution-side and residual-side training dynamics during optimization.

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